<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA<sup>®</sup> 9.0.</p>
A numerical study has been carried out to investigate heat transfer by natural convection and radiation under the effect of magnetohydrodynamic (MHD) for steady state axisymmetric twodimensional laminar flow in a vertical cylindrical channel filled with saturated porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 programming. The parameters affected on the system are Rayl
... Show MoreIn this research the natural frequency of a cracked simple supported beam (the crack is in many places and in different depths) is investigated analytically, experimentally and numerically by ANSYS program, and the results are compared. The beam is made of iron with dimensions of L*W*H= (0.84*0.02* 0.02m), and density = 7680kg/m3, E=200Gpa. A comparison made between analytical results from ANSYS with experimental results, where the biggest error percentage is about (7.2 %) in crack position (42 cm) and (6 mm) depth. Between Rayleigh method with experimental results the biggest error percentage is about (6.4 %) for the same crack position and depth. From the error percentages it could be concluded that the Rayleigh method gives
... Show MoreThis paper presents a comprehensive numerical analysis of the improvement in bearing capacity and settlement performance of hexagonal shallow footings with inclined skirts. Various numerical analyses were conducted using PLAXIS 3D to investigate the influence of skirt length-to-footing width (L/B) ratios and skirt inclination angles (θ) on hexagonal footings in loose sand. The models showed very good agreement with experimental data reported in previous studies, with an R² value of 0.996 and a maximum error of less than 4.31%. It was concluded that the inclusion of inclined skirts has a positive effect on bearing capacity, increasing it by up to approximately 2.97 times compared to non-inclined configurations, while significantly
... Show MoreIn this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.
Water supply networks are marred by serious risks of imperceptible pipeline leakage, posing sustainability and performance threats. This article highlights the use of vibratory signal features to get around the drawbacks of traditional methods in a highly detailed framework for leak detection based on CatBoost. demonstrated excellent diagnostic performance and carried out a thorough test performance evaluation on five leakage configurations . The expected system achieved an accuracy of 98.1% (variance (well within x/3% of expected):, beating traditional competitors such as Random Forest (97.3%) and Support Vector Machine (93.8%). For example, the area under the receiver-operating characteristic curve was 0.995, in
... Show MoreTwo homopolymeric and three copolymeric additives for base oil were synthesized using octyl acrylate (OA) and tert-butyl acrylamide (TBA) monomers. The two additives named P1 and P2 are the homopolymers of TBA and OA, respectively, whereas copolymeric additives named Co1, Co2, and Co3 were synthesized by varying the ratios of TBA:OA as 1:3, 3:1 and 1:1, respectively. The prepared polymers were characterized by Fourier Transform Infrared (FTIR). Based on the solubility of synthesized polymers in base oil and reactivity ratios of TBA/OA copolymer (0.222, 0.434) calculated by Fineman-Ross method, P2, Co1, Co2 and Co3 were selected to evaluate their performance as pour point depressant (PPD), viscosity improver (VII), and anticorrosion addit
... Show MoreThe present work elucidates the utilization of activated carbon (AC) and activated carbon loaded with silver nanoparticles (AgNPs-AC) to remove tetracycline (TC) from synthetically polluted water. The activated carbon was prepared from tea residue and loaded with silver nanoparticles. Scanning electron microscopy (SEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and Brunauer-Emmett-Teller (BET) were used to characterize the activated carbon (AC) and silver nanoparticles-loaded activated carbon (AgNPs-AC). The impact of various parameters on the adsorption effectiveness of TC was examined. These variables were the initial adsorbate concentration (Co), solution acidity (pH), adsorption time (t), and dosag
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